BuddyPress.org

@alwaysalready Thank you so much!!!!!
Your solution sorted everything. I so appreciate it!!!!!!!!!!!!!!!

In case it is interesting to anyone, to try fix this before coming to this thread, I:
1. installed “Check Email” to see if there was a problem sending emails from my site (there wasn’t)
2. installed “WP Mail SMTP”, setting up SMTP with all its complications in case it was some sort of spam issue (it wasn’t)
3. discovered using the above that the registration emails were being bounced with the error message “Diagnostic-Code: smtp; 550 Messages should have one or no To headers, not 2.” When I looked at the headers, sure enough, there were two “To: destination-email-address” lines in the header.
4. Deactivated BuddyPress. Found that registration emails successfully went through.
5. Finally came here, having found out that BuddyPress was definitely the culprit.

All this has been quite stressful, it is the first website I’ve ever set up.

@alwaysalready – thanks for posting your solution.
Perhaps you could convert your blog article into a page in the codex.

I found a way to resolve this problem using a mixture of ideas others have shared (including @6logics and @loveplove). I’ve put the details in a blog post here. In summary, what worked for me was the following in the bp-custom.php file:

// Set BP to use wp_mail
add_filter( 'bp_email_use_wp_mail', '__return_true' );
 
// Set messages to HTML
remove_filter( 'wp_mail_content_type', 'set_html_content_type' );
add_filter( 'wp_mail_content_type', 'set_html_content_type' );
function set_html_content_type() {
    return 'text/html';
}
 
// Use HTML template
add_filter( 'bp_email_get_content_plaintext', 'get_bp_email_content_plaintext', 10, 4 );
function get_bp_email_content_plaintext( $content = '', $property = 'content_plaintext', $transform = 'replace-tokens', $bp_email ) {
    if ( ! did_action( 'bp_send_email' ) ) {
        return $content;
    }
    return $bp_email->get_template( 'add-content' );
}
//Optionally remove the filter above after it's run
remove_filter('wp_mail','redirect_mails',20);
 
// Optionally change your email address
add_filter('wp_mail_from','noreply_from');
function noreply_from($from) {
  return 'noreply@YOUR_DOMAIN.org'; //Replace 'YOUR_DOMAIN.org' with email address
}

// Optionally change your from name
add_filter('wp_mail_from_name','noreply_from_name');
function noreply_from_name($name) {
    return 'YOUR_DOMAIN No-Reply'; //Replace 'YOUR_DOMAIN No-Reply' with the from name
}

I found a way to resolve this problem using a mixture of ideas others have shared elsewhere. I’ve put the details in a blog post here. In summary, what worked for me was the following in the bp-custom.php file:

// Set BP to use wp_mail
add_filter( 'bp_email_use_wp_mail', '__return_true' );
 
// Set messages to HTML
remove_filter( 'wp_mail_content_type', 'set_html_content_type' );
add_filter( 'wp_mail_content_type', 'set_html_content_type' );
function set_html_content_type() {
    return 'text/html';
}
 
// Use HTML template
add_filter( 'bp_email_get_content_plaintext', 'get_bp_email_content_plaintext', 10, 4 );
function get_bp_email_content_plaintext( $content = '', $property = 'content_plaintext', $transform = 'replace-tokens', $bp_email ) {
    if ( ! did_action( 'bp_send_email' ) ) {
        return $content;
    }
    return $bp_email->get_template( 'add-content' );
}
//Optionally remove the filter above after it's run
remove_filter('wp_mail','redirect_mails',20);
 
// Optionally change your email address
add_filter('wp_mail_from','noreply_from');
function noreply_from($from) {
  return 'noreply@YOUR_DOMAIN.org'; //Replace 'YOUR_DOMAIN.org' with email address
}

// Optionally change your from name
add_filter('wp_mail_from_name','noreply_from_name');
function noreply_from_name($name) {
    return 'YOUR_DOMAIN No-Reply'; //Replace 'YOUR_DOMAIN No-Reply' with the from name
}

I found a way to resolve this problem using a mixture of ideas, including the suggestions from @bharat and @vbnr. I’ve put the details in a blog post here. In summary, what worked for me was the following in the bp-custom.php file:

// Set BP to use wp_mail
add_filter( 'bp_email_use_wp_mail', '__return_true' );
 
// Set messages to HTML
remove_filter( 'wp_mail_content_type', 'set_html_content_type' );
add_filter( 'wp_mail_content_type', 'set_html_content_type' );
function set_html_content_type() {
    return 'text/html';
}
 
// Use HTML template
add_filter( 'bp_email_get_content_plaintext', 'get_bp_email_content_plaintext', 10, 4 );
function get_bp_email_content_plaintext( $content = '', $property = 'content_plaintext', $transform = 'replace-tokens', $bp_email ) {
    if ( ! did_action( 'bp_send_email' ) ) {
        return $content;
    }
    return $bp_email->get_template( 'add-content' );
}
 
// Optionally change your email address and from name.
add_filter('wp_mail_from','noreply_from');
function noreply_from($from) {
  return 'noreply@YOUR_DOMAIN.org'; //Replace 'YOUR_DOMAIN.org' with email address
}
 
add_filter('wp_mail_from_name','noreply_from_name');
function noreply_from_name($name) {
    return 'YOUR_DOMAIN No-Reply'; //Replace 'YOUR_DOMAIN No-Reply' with the from name
}

You could override the template to showcase your own unique one. Here’s some more info on it.

Theme Compatibility & Template Files

BuddyPress uses its own email api.
This codex page has info re customization.

Emails

@xpc33 Try https://wbcomdesigns.com/downloads/buddypress-redirect/

Just create WP pages and leave them blank.
Then assign them on the screen shown in your shared img.

Register and Activation Pages